7th ISF

MATH013 - Popoviciu’s Inequality in 2 Dimensions

Convex function is one of interesting function which has the property that if f is convex function then f (tx + (1 - t)y) ≤ tf (x) + (1 - t)f (y) for all x,y E I and all t E [0,1]. Popoviciu inequalit y is one of inequality f ( (x+y)/2)+ f ( (y+z)/2)+ f ( (z+x)/2) ≤ 3/2 f ((x + y + z )/3)+1/2(f (x) + f (y) + f (z)). It was studied in term of convex function , it can prove by using convex function property which we will study in 2 dimensions. Coordinated convex function was defined as convex in 2 dimension. f (tx + (1 - t)y,sw + (1 - s)z) ≤tsf (x,w) + t(1 - s)f (x,z)+s(1 - t)f (y,w) + (1 - t)(1 - s)f (y,z) for all (x,y),(w,z) ∈ ∆ which ∆ is convex set. In this paper we will prove Popoviciu for coordinated including other version of this inequality

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